INF 5490 RF MEMS. LN12: RF MEMS inductors. Spring 2011, Oddvar Søråsen Department of informatics, UoO

Transcription

1 INF 5490 RF MEMS LN12: RF MEMS inductors Spring 2011, Oddvar Søråsen Department of informatics, UoO 1

2 Today s lecture What is an inductor? MEMS -implemented inductors Modeling Different types of RF MEMS inductors Horizontal plane inductors Real solenoids How to increase performance Q-value, Inductance (L), Self resonance frequency (f_max) Elevated inductors Inductor banks 2

3 What is an inductor? Inductor = a component with interaction between magnetic and electric flux Magnetic field current Two basic laws Faraday s law Varying magnetic field induces current Ampere s law Current flowing sets up a magnetic field 3

4 Faraday s law magnetic flux density permeability magnetic field 4

5 Ampere s law 5

6 Inductors follow Faraday s/ampere s laws Change of current in inductor Change of magnetic field (Ampere s law) Electric field induced (Faraday s law) The induced electric field opposes further change in current (Lenz law) Inertia with respect to variation: reactance Mechanical analogy: mass! 6

7 Inductors Generally implemented as solenoids 2D (in plane) or 3D Several turns used to increase magnetic flux density May give large inductance, L, for a small area/volume Basic equations V = L di/dt V = Ls * I (Laplace) metal dielectric substrate Solenoids in plane are typical for IC and MEMS 7

8 Competition from IC Standard CMOS, SiGe-technology has given good results! F.ex. Q = 12 2 GHz, 16 6 GHz (2003) Reasons for the increased IC-component performance which has been obtained Optimized inductor geometry due to good CAD tools Using thick metal layers of gold (3 μm) Using thick dielectric (3-6 μm oxide over substrate) Using high resistivity substrate, ohm-cm Reducing eddy currents = magnetic induced currents Thereby reducing substrate loss underneath the inductor 8

9 Any reason for RF MEMS inductors? Micromachined inductors should have better performance than todays CMOS inductors MEMS may give higher Q-values! Q>30 MEMS may give higher L and self resonancefrequency Should be CMOS compatible F.ex. post processing CMOS L L, C, R -circuit Micromachined inductances not yet a commercial product 9

10 Applications of (RF MEMS) inductors Replacement components in Low noise oscillators Integrated LC-filters Amplifiers On-chip matching networks Impedance transformers Phase shifters 10

11 RF MEMS inductors Two-dimensional (planar) inductors Three-dimensional inductors, solenoids Only fixed-value inductors can be implemented No practical implementation of tunable inductors exist Variable inductance values: implemented as an inductor bank Many inductors with fixed, high Q-values In combination with MEMS contact switches 11

12 Planar inductors, in general Implemented in a single plane One metal layer patterned by etching Inductor rests on a substrate covered by a dielectric Loss in inductor due to: Finite metal conductivity Loss in dielectric Loss in substrate Area limitations for RF metal dielectric substrate Total length of an inductor has to be significantly shorter than the wavelength This will give negligible phase shift of signal 12

13 Contribution to inductance Self inductance from its own winding Mutual inductance from neighbouring windings Mutual coupling between neighbour lines Total inductance is the sum of self inductance and mutual inductance In some elements current flows in the same direction, in others opposite 13

14 Different planar geometries Simple line sections Each one has a low inductance value, nh Meander Coupling by negative mutual inductances Spiral inductors Increasing inductance, L Problem: connecting to the inner winding Wire bonding Separate structure layer Flip-chip bonding methods 14

15 Different planar geometries Distance between lines is critical Circular spiral has a shorter length than a quadratic spiral Lower R Q is about 10% higher with same diameter, d0 Higher Q achieved by increasing number of turns per area Self resonance frequency decreases due to the increase in capacitance limits the region of use 15

16 Inductor is a non-ideal component Changes its value versus frequency Becomes capacitive at high frequencies 16

17 General model for a planar inductor Ls is low frequency inductance Rs is series resistance Cs is capacitance between windings C1 is capacitance in oxide layer between inductor and substrate Cp is capacitance to ground through substrate Rp is eddy current loss in substrate 17

18 Frequency response for a planar inductor At low frequencies we have At high frequencies: Rp1 is negligible C1 and Cp1 combined Cp X X X 18

19 Parallel resonator Due to parasitic capacitances a specific self resonance frequency is obtained Q_ind = ωl/r At resonance: 19

20 Ex.: Inductor reactance Resistance is here defined at 2 GHz R is supposed to vary as sqrt (f) above 2 GHz due to the skin effect Parallel-type resonance at 8 GHz, phase also changes At resonance the input impedance of a parallel resonator is real and given by: Figure shows that simple L, R model is valid to 0.5 f_resonance Phase properties show that the component is inductive also for higher frequencies 20

21 Today s lecture What is an inductor? MEMS -implemented inductors Modeling Different types of RF MEMS inductors Horizontal plane inductors Real solenoids How to increase performance Q-value, Inductance (L), Self resonance frequency (f_max) Elevated inductors Inductor banks 21

22 Example: Thick copper/polyimide horizontal-plane inductor Form ( mold ) of organic material Ionescu, EPFL 22

23 Ex. CMOS MEMS inductor High Q, 6 Cu layers Low-ε dielectric Post-CMOS processing Standard CMOS + RIE post processing + isotropic etch X. Zhu et al Carnegie Mellon University Ex. from Transducers 2001 Anisotropic etching followed by isotropic etching Top metal layer is mask 23

24 Ex. Spiral inductor (Ahn & Allen) Two solenoids Magnetic core used for trapping magnetic flux Must be a high permeability material Ex. Varadan fig. 4.7 (Ahn & Allen) Conductor from centre needed! 24

25 Effect of magnetic core Magnetic core increases inductance 25

26 Meander inductors Meander has lower inductance than spiral inductor Meander fabricated by surface processing a) Metal conductor in one layer Penetrated by multilevel magnetic core b) Schematic of principle Ala magnetic core in one layer surrounded by metal turns 26

27 Meander fabricated (SEM picture) 27

28 Meander: effect of different line widths Influence of the line width (C vs width) sheet resistance is inversely proportional to w decreases! Resistance decreases if w increases, but the capacitance increases dc = distance between conductors (line spacing) 28

29 Effect of stripe width w on Q-factor Different frequencies Optimal values of w exist for minimizing series resistance and maximizing Q 29

30 Optimization Width of each turn can be optimized Each turn has a constant resistance 30

31 Effect of different implementations How line spacing influences L Line spacing has different effect for spiral and meander: constructive versus destructive mutual inductance 31

32 Effect of number of turns on L and Q Spiral inductors with same dimensions n: 3 8: L increases Q decreases (due to increase in C) f_max decreases 32

33 Solenoid-type inductors Classical example Process using thick photoresist mold μm deep Top fabricated using copper: electroplating seed μm copper layer plated on top Result: loops formed 33

34 Solenoid-type copper inductors Si or glass substrate give different values Results from Yoon et al. 34

35 Extreme type Solenoid-type inductor with large alumina core Placed manually on a Si-substrate, fig. Cross section 650 x 500 μm2 Photo resist on alumina core Direct write laser, 3D Electroplating 5-10 μm copper Not practical! Young et al.,

36 Example of 3-D structure Difficult to produce Nickel-iron (permalloy) magnetic core Multilevel copper + viacontacts Contacts have high contact resistance Need of many turns to get high L More contacts higher resistance Electroplating of metal lines and via holes may reduce resistance and increase performance Ahn & Allen,

37 Today s lecture What is an inductor? MEMS -implemented inductors Modeling Different types of RF MEMS inductors Horizontal plane inductors Real solenoids How to increase performance Q-value, Inductance (L), Self resonance frequency (f_max) Elevated inductors Inductor banks 37

38 Q-factor depends on resistive loss and substrate loss For low frequencies: resistive loss limits Q For high frequencies: substrate loss limits Q 38

39 Improving Q-factor Metallization is important Reduction of resistive loss! Use metals with higher conductivity Use copper, Cu, instead of Al Use thicker structures 39

40 Effect of metal thickness Series resistance limits performance Simulations show that minimum thickness of 2 x skin depth is needed to obtain minimum resistance resistivity Resistance per length skin depth µ = permeability ρ = resistivity 40

41 Thick conductors needed For copper at 1 GHz: skin depth is about 2 μm One should have conductors of min 2 x skin depth thickness E.g. about 4-5 μm for Cu Thick layer! Typically obtained by electroplating 41

42 Change of Q versus metal thickness 42

43 Double level metallization 4.5 μm 9 μm ( normal/q-enhanced ) with/without 10 μm polyimide layer ( suspended/on Si ) 43

44 Substrate etching Parasitic capacitance between inductor and ground plane is a problem Depends on type and thickness of dielectric Depends on type and thickness of substrate Solution: etching of the underlying substrate Reduction of parasitic capacitance Q increases Resonance frequency is shifted to higher frequency Increases the useful bandwidth of the inductor High L can be implemented at the same time as avoiding a too low f_max Alternative: elevation/suspension 44

45 Substrate capacitance effect on Q and reactance X At 1 4 GHz series resitance limits Figure shows that higher Q also gives a higher self resonance frequency 45

46 With and without underlying substrate 46

47 Test system Example system for testing the effect of having a solenoid on a membrane or directly on Si 47

48 Achieved L on Si and membrane M = membrane, S = Si 48

49 Ex.: Q for different etch depths 49

50 Different substrate materials Substrate etching has no effect on Q for low frequencies Rs is the limitation Rs is prop with sqrt(f) Look at the effect of different substrate materials Different resistivity 50

51 Q-factor for substrates with different resistivities Eddy current -effects are present at high frequency High resistivity substrate increases performance Both rectangular and spiral inductors are shown 51

52 Air gap - inductor Thick metal planar inductor over substrate with an air gap in-between Elimination of substrate coupling: 30 μm elevation Sacrificial metallic mold (SMM) process used μm copper layer 52

53 Performance to inductor above air gap 53

54 Classical examples Ex. from the first known work, fig 12.8 a: anisotropic etching Fig 12.8 b: suspended inductor One anchor: sensitive to mechanical vibrations Q = 17 at 8.6 GHz 54

55 Air-gap for solenoids Schematic figure! 55

56 Effect of air-gap for spiral inductors L benefits from no-gap (between inductor and substrate), Q benefits from air-gap 56

57 Summary: How to increase performance? Have thick metal layer with good conductivity To reduce series resistance Use substrate etching Reduce substrate parasitic capacitance Use 3-D structures For vertical plane solenoids the L-value may increase Use of core material 57

58 Basic implementation technologies Thick metal electroplating GHz Substrate etching GHz Three-dimensional solenoid type inductors GHz Self-assembly (elevation) of inductor Elevate inductor above substrate to reduce parasitic capacitance to substrate, GHz 58

59 Folded and elevated inductors Solder surface tension Eric. Yeatman, Imperial College, London 59

60 Out of plane inductors Inductor can be elevated by scratch actuators L. Fan et al, MEMS 1998 Elevated 250 μm over Si substrate Resonance at GHz after elevation of solenoid 60

61 Micromachining using self-assembly Elevate inductor above substrate to reduce parasitic capacitance Cr-Au layer over polylayer Different residual stress in materials make the inductor curl above substrate Anchor causes a significant parasitic capacitance 61

62 Solder surface tension used Photo resist as sacrificial layer Copper structure with solder pads between anchor and a free movable structure Heating to 185 C solder pads melt and pull, due to surface tension force, the structure to a vertical position Cooling solder hardens 62

63 Structure with suspension hinges Copper structure can manually be folded and glued Typical turns with large dimensions ~100 μm M. Gel et al, Transducers

64 Today s lecture What is an inductor? MEMS -implemented inductors Modeling Different types of RF MEMS inductors Horizontal plane inductors Real solenoids How to increase performance Q-value, Inductance (L), Self resonance frequency (f_max) Elevated inductors Inductor banks 64

65 Programmable inductor banks Thermal actuation! [Ionescu] 65

66 How different design parameters influence performance Q_max and f_rez decrease when area and number of turns increase (Double arrow: less influence) 66